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arithmetic progressions one of the

ARITHMETIC PROGRESSIONS: One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories

Examples:

The fourth term of an AP is 0. Prove that its 25th term is triple its 11th term.

Ans: a₄= 0

⇒ a + 3d = 0

T.P a₂₅= 3 (a11)

⇒ a + 24d = 3 (a + 10d)

⇒ a + 24d = 3a + 30d

RHS sub a = - 3d

- 3d + 24d = 21d

LHS 3a + 30d

- 9d + 30d = 21d

LHS = RHS Hence proved

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